Yes, she was a mathematician. If you have a specific question then please ask it but don't just stack a few words and assume that it makes a sensible question.
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She is probably best known for her work on partial differential equations. Her paper on the subject contains what is now known as the Cauchy–Kovalevskaya theorem, which gives conditions under which a certain class of those equations does have solutions.For her doctorate she also presented papers, at the University of Göttingen, on the dynamics of Saturn's rings and on elliptic integrals.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
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